Discussiones Mathematicae Graph Theory最新文献_第7页

Dominated Pair Degree Sum Conditions of Supereulerian Digraphs 超欧拉有向图的控制对度和条件

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-18 DOI: 10.7151/dmgt.2476

Changchang Dong, J. Meng, Juan Liu

引用次数: 0

On Proper 2-Labellings Distinguishing by Sums, Multisets or Products 用和、多集或积来区分适当的2-标记

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-18 DOI: 10.7151/dmgt.2473

Julien Bensmail, Foivos Fioravantes

{"title":"On Proper 2-Labellings Distinguishing by Sums, Multisets or Products","authors":"Julien Bensmail, Foivos Fioravantes","doi":"10.7151/dmgt.2473","DOIUrl":"https://doi.org/10.7151/dmgt.2473","url":null,"abstract":"Abstract Given a graph G, a k-labelling ℓ of G is an assignment ℓ : E(G) → {1, . . . , k} of labels from {1, . . . , k} to the edges. We say that ℓ is s-proper, m-proper or p-proper, if no two adjacent vertices of G are incident to the same sum, multiset or product, respectively, of labels. Proper labellings are part of the field of distinguishing labellings, and have been receiving quite some attention over the last decades, in particular in the context of the well-known 1-2-3 Conjecture. In recent years, quite some progress was made towards the main questions of the field, with, notably, the analogues of the 1-2-3 Conjecture for m-proper and p-proper labellings being solved. This followed mainly from a better global understanding of these types of labellings. In this note, we focus on a question raised by Paramaguru and Sampathkumar, who asked whether graphs with m-proper 2-labellings always admit s-proper 2-labellings. A negative answer to this question was recently given by Luiz, who provided infinite families of counterexamples. We give a more general result, showing that recognising graphs with m-proper 2-labellings but no s-proper 2-labellings is an NP-hard problem. We also prove a similar result for m-proper 2-labellings and p-proper 2-labellings, and raise a few directions for further work on the topic.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43164988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Walk Domination: Weakly Toll Domination, l2 and l3 Domination 关于步行统治:弱收费统治，l2和l3统治

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-18 DOI: 10.7151/dmgt.2475

M. Gutierrez, S. Tondato

引用次数: 0

The Generalized 3-Connectivity and 4-Connectivity of Crossed Cube 交叉立方体的广义3-连通性和4-连通性

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-18 DOI: 10.7151/dmgt.2474

Heqin Liu, Dongqin Cheng

引用次数: 1

The Matching Extendability of 7-Connected Maximal 1-Plane Graphs 7-连通极大1-平面图的匹配可扩展性

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-09-30 DOI: 10.7151/dmgt.2470

Yuanqiu Huang, Licheng Zhang, Yuxi Wang

引用次数: 2

A σ3 Condition for Arbitrarily Partitionable Graphs 任意可分图的σ3条件

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-09-30 DOI: 10.7151/dmgt.2471

Julien Bensmail

{"title":"A σ3 Condition for Arbitrarily Partitionable Graphs","authors":"Julien Bensmail","doi":"10.7151/dmgt.2471","DOIUrl":"https://doi.org/10.7151/dmgt.2471","url":null,"abstract":"Abstract A graph G of order n is arbitrarily partitionable (AP for short) if, for every partition (λ1, . . ., λp) of n, there is a partition (V1, . . ., Vp) of V (G) such that G[Vi] is a connected graph of order λi for every i ∈ {1, . . ., p}. Several aspects of AP graphs have been investigated to date, including their connection to Hamiltonian graphs and traceable graphs. Every traceable graph (and, thus, Hamiltonian graph) is indeed known to be AP, and a line of research on AP graphs is thus about weakening, to APness, known sufficient conditions for graphs to be Hamiltonian or traceable. In this work, we provide a sufficient condition for APness involving the parameter ̄σ3, where, for a given graph G, the parameter ̄σ3(G) is defined as the minimum value of d(u) + d(v) + d(w) − |N(u) ∩ N(v) ∩ N(w)| for a set {u, v, w} of three pairwise independent vertices u, v, and w of G. Flandrin, Jung, and Li proved that any graph G of order n is Hamitonian provided G is 2-connected and ̄σ3(G) ≥ n, and traceable provided ̄σ3(G) ≥ n − 1. Unfortunately, we exhibit examples showing that having ̄σ3(G) ≥ n − 2 is not a guarantee for G to be AP. However, we prove that G is AP provided G is 2-connected, ̄σ3(G) ≥ n−2, and G has a perfect matching or quasi-perfect matching.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42234706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Strong Path Partition Conjecture 关于强路径划分猜想

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-09-30 DOI: 10.7151/dmgt.2468

J. de Wet, M. Frick, O. Oellermann, Jean E. Dunbar

引用次数: 0

Resistance in Regular Class Two Graphs 正则第二类图中的阻力

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-09-30 DOI: 10.7151/dmgt.2467

I. Allie, Jordan Arenstein

{"title":"Resistance in Regular Class Two Graphs","authors":"I. Allie, Jordan Arenstein","doi":"10.7151/dmgt.2467","DOIUrl":"https://doi.org/10.7151/dmgt.2467","url":null,"abstract":"Abstract A well-known theorem of Vizing separates graphs into two classes: those which admit proper Δ-edge-colourings, known as class one graphs; and those which do not, known as class two graphs. Class two graphs do admit proper (Δ+ 1)-edge-colourings. In the context of snarks (class two cubic graphs), there has recently been much focus on parameters which are said to measure how far the snark is from being 3-edge-colourable, and there are thus many well-known lemmas and results which are widely used in the study of snarks. These parameters, or so-called measurements of uncolourability, have thus far evaded consideration in the general case of k-regular class two graphs for k > 3. Two such measures are the resistance and vertex resistance of a graph. For a graph G, the (vertex) resistance of G, denoted as (rv(G)) r(G), is defined as the minimum number of (vertices) edges which need to be removed from G in order to render it class one. In this paper, we generalise some of the well-known lemmas and results to the k-regular case. For the main result of this paper, we generalise the known fact that r(G) = rv(G) if G is a snark by proving the following bounds for k-regular G:rv(G)≤r(G)≤⌊ k2 ⌋rv(G) G:{r_v}left( G right) le rleft( G right) le leftlfloor {{k over 2}} rightrfloor {r_v}left( G right) . Moreover, we show that both bounds are best possible for any even k.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44092524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Connectedness and cycle spaces of friends-and-strangers graphs 朋友-陌生人图的连通性和循环空间

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-09-04 DOI: 10.7151/dmgt.2492

Colin Defant, David Dong, Alan Lee, Michelle Wei

{"title":"Connectedness and cycle spaces of friends-and-strangers graphs","authors":"Colin Defant, David Dong, Alan Lee, Michelle Wei","doi":"10.7151/dmgt.2492","DOIUrl":"https://doi.org/10.7151/dmgt.2492","url":null,"abstract":"If $X=(V(X),E(X))$ and $Y=(V(Y),E(Y))$ are $n$-vertex graphs, then their friends-and-strangers graph $mathsf{FS}(X,Y)$ is the graph whose vertices are the bijections from $V(X)$ to $V(Y)$ in which two bijections $sigma$ and $sigma'$ are adjacent if and only if there is an edge ${a,b}in E(X)$ such that ${sigma(a),sigma(b)}in E(Y)$ and $sigma'=sigmacirc (a,,b)$, where $(a,,b)$ is the permutation of $V(X)$ that swaps $a$ and $b$. We prove general theorems that provide necessary and/or sufficient conditions for $mathsf{FS}(X,Y)$ to be connected. As a corollary, we obtain a complete characterization of the graphs $Y$ such that $mathsf{FS}(mathsf{Dand}_{k,n},Y)$ is connected, where $mathsf{Dand}_{k,n}$ is a dandelion graph; this substantially generalizes a theorem of the first author and Kravitz in the case $k=3$. For specific choices of $Y$, we characterize the spider graphs $X$ such that $mathsf{FS}(X,Y)$ is connected. In a different vein, we study the cycle spaces of friends-and-strangers graphs. Naatz proved that if $X$ is a path graph, then the cycle space of $mathsf{FS}(X,Y)$ is spanned by $4$-cycles and $6$-cycles; we show that the same statement holds when $X$ is a cycle and $Y$ has domination number at least $3$. When $X$ is a cycle and $Y$ has domination number at least $2$, our proof sheds light on how walks in $mathsf{FS}(X,Y)$ behave under certain Coxeter moves.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41527870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

On the vertex position number of graphs 图的顶点位置数

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-09-01 DOI: 10.7151/dmgt.2491

Maya G. S. Thankachy, Ullas Chandran S.V., J. Tuite, Elias John Thomas, Gabriele Di Stefano, G. Erskine

引用次数: 1